The total cost bounds of the transportation problem with varying demand and supply

A transportation problem is a linear programming problem based on a network structure consisting of a finite numbers of nodes and arcs attached to them. In real world applications, the supply and demand quantities in the transportation problem are sometimes hardly specified precisely because of changing economic conditions. This paper investigates the transportation problem when the demand and supply quantities are varying. A pair of mathematical programs is formulated to calculate the objective value. The derived result is also in range, where the total transportation cost would appear. In addition to allowing for simultaneous changes in supply and demand values, the total cost bounds are calculated directly. Due to the structure of the transportation problem, the largest total transportation cost may not occur at the highest total quantities shipped. Since the total cost bounds are derived, it would be beneficial to decision-making.